Thursday, May 28, 2009

I do not know what it is about those Subs

As I was eating at Subway today, I started to think about how many possible combinations of sandwiches you could create.

Someone may note that I have more posts inspired by sports and subway...

Anyway, in order to be a sandwich, you need bread. There are 7 or 8 bread choices.
On the website I see 21 permanent meat choices. (Includes veggie, which is the choice of no meat.)
The subway by my office has 3 kinds of cheese. 4 choices if you get no cheese, but 7 with 2 cheese options and 8 cheese combinations if you include no, one, two or all choices of cheese. (2 to the 3rd power.) Has anyone ever asked for multiple cheeses? I think I want to next time.
Toasted or Not. Mutliply by two.
I believe there are 9 veggie choices. I think the easiest way to do this is to raise two to the ninth power because you can get multiple veggies.
Then there are 8 dressing choices, wait, 9 because you can get oil OR vinegar. Again, multiple dressings is also an option.
Salt and pepper comes in one can so thats another times binary multiplier. 
Parmesean cheese sprinkle? Another two. 

So if my memory and math serves me right, that is 8*21*8*2*(2^9)*(2^9)*2*2 
And that is assuming you do not get multiple meat orders. I may try that next time too, "I would like ham, turkey and meatball marina sub please. Toast it. With pepperjack and provolone."

You could bound the options by only allowing choices that have no effect on the price (post-meat selection). I do not know if multiple cheeses increases the price, I am sure that multiple meats would. I also like to get my onions and peppers toasted with the rest of the sub -- that option is free, but not included in my combination calculation. For the sake of simplicity I will say that a sub with toasted onions and peppers is the same as non-toasted.

My product is 2,818,572,288 combinations. If you ate at subway once per day and chose a unique combination, it would take you 7,722,116 years before you ate them all. If you ate 3 times a day that is still 2.6 million years. How about 5 meals a day, all subway: Only 1.5 million years. 

I think my favorite combinations would coincide with the most hungry days: Veggie sub, no veggies, no dressing. You would only have to eat plain toast or bread 16 times. 


  1. By the way, I think this would be an awesome high school stats class homework assignment. Go onto the subway website and find out how many combinations of subway sandwiches you could make.
    Let them justify their answers by defining what a sandwich is and showing their work.

  2. I've gotten multiple cheeses, they charge extra.

    You should be a math teacher.